Bayesian Feature Selection in Joint Quantile Time Series Analysis

TL;DR

This paper introduces a Bayesian feature selection method for high-dimensional joint quantile time series analysis, offering a flexible, interpretable, and efficient approach suitable for small datasets with superior performance.

Contribution

It proposes the QFSTS model, a novel Bayesian structural time series framework that enables effective feature selection and interpretation in multivariate quantile time series.

Findings

QFSTS outperforms existing methods in feature selection accuracy.

The model provides fast convergence with small datasets.

It achieves superior forecasting and parameter estimation.

Abstract

Quantile feature selection over correlated multivariate time series data has always been a methodological challenge and is an open problem. In this paper, we propose a general Bayesian dimension reduction methodology for feature selection in high-dimensional joint quantile time series analysis, under the name of the quantile feature selection time series (QFSTS) model. The QFSTS model is a general structural time series model, where each component yields an additive contribution to the time series modeling with direct interpretations. Its flexibility is compound in the sense that users can add/deduct components for each time series and each time series can have its own specific valued components of different sizes. Feature selection is conducted in the quantile regression component, where each time series has its own pool of contemporaneous external predictors allowing nowcasting. Bayesian methodology in extending feature selection to the quantile time series research area is developed using multivariate asymmetric Laplace distribution, spike-and-slab prior setup, the Metropolis-Hastings algorithm, and the Bayesian model averaging technique, all implemented consistently in the Bayesian paradigm. The QFSTS model requires small datasets to train and converges fast. Extensive examinations confirmed that the QFSTS model has superior performance in feature selection, parameter estimation, and forecast.